

A038050


Number of labeled rooted trees with 3colored leaves.


2



3, 6, 45, 504, 7785, 153468, 3681909, 104126256, 3392064945, 125089571700, 5151335388309, 234322765501608, 11668410187187481, 631335472193760012, 36881146426978035765, 2313552152470193124192, 155107536736245864549345
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OFFSET

1,1


REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and TreeLike Structures, Cambridge, 1998, p. 185 (3.1.83)


LINKS

Table of n, a(n) for n=1..17.
Index entries for sequences related to rooted trees
N. J. A. Sloane, Transforms


FORMULA

Divides by n and shifts left under exponential transform.
E.g.f.: 2*x  LambertW(x*exp(2*x)).  Vladeta Jovovic, Mar 09 2003
a(n) = Sum_{k=0..n} (binomial(n, k)*2^k*(nk)^(n1)).
a(n) ~ sqrt(1+LambertW(2*exp(1))) * (2*exp(1)/LambertW(2*exp(1)))^n * n^(n1).  Vaclav Kotesovec, Oct 05 2013


MATHEMATICA

Rest[CoefficientList[Series[2*xLambertW[x*E^(2*x)], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 05 2013 *)


CROSSREFS

Cf. A000169, A029857.
Cf. A038049.
Sequence in context: A203434 A076170 A137775 * A194080 A261841 A197884
Adjacent sequences: A038047 A038048 A038049 * A038051 A038052 A038053


KEYWORD

nonn,eigen


AUTHOR

Christian G. Bower, Jan 04 1999


STATUS

approved



